The function f is one to one. Find the inverse of the function. find the domain and range of f and f inverse?

Posted on Jul 01, 2008 under domain news and reports | 4 Comments

f(x) = (2-x)/(3+x)

4 Responses to “The function f is one to one. Find the inverse of the function. find the domain and range of f and f inverse?”

  1. Anime Lover Says:

    f inverse = interchange x and y and solve x in terms of y
    domain = all real numbers

  2. notthejake Says:

    domain of f(x) is x doesn't equal -3
    range of f^-1(x) is y doesn't equal -3

    range of f(x) is y doesn't equal -1
    domain of f^-1(x) is x doesn't equal -1

    to find inverse: solve x = (2 – y) / (3 + y) for y

    x(3 +y) = 2 – y
    3x + xy = 2 – y
    y + xy = 2 – 3x
    y(1 + x) = 2 – 3x
    y = f^-1(x) = (2 – 3x) / (1 + x)
    domain of f^-1(x): x doesn't equal -1 (range of f(x): y <>-1)
    range of f^-1(x): y doesn't equal -3 (domain of f(x): x <>-3)

    check: find f(-2) = (2 – -2) / (3 + -2) = 4/1 = 4
    now find f^-1(4) = (2 – 3(4)) / (1 + 4) = -10 / 5 = -2
    so (-2,4) on f(x); (4, -2) on f^-1(x) check

  3. phoenixstarshine Says:

    (2-y)/(3+y)=x
    2-y=3x+xy
    xy+y=2-3x
    y(x+1)=2-3x
    y=(2-3x)/(x+1)

    dom f=x <>-3, dom f^-1=x<>-1, where '<>'means "not equal to"

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